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Journal of Mathematical Physics

Fluctuation properties of the imperfect Bose gas

E. Buffet, Joseph V. Pulé

Published Jun 1, 1983• 71 citations
Publisher

Abstract

The fluctuations of the occupation numbers of the different levels of the imperfect Bose gas are computed. They are neither normal, Gaussian, nor independent of the way the infinite volume limit is taken. The fluctuations of the overall density are on the contrary normal, Gaussian, and shape independent.
DOI
10.1063/1.525855

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The field fluctuations are studied for the free and imperfect Bose gas. In the phase where there is condensation, these field fluctuations are abnormal, with critical exponents depending on the way the symmetry-breaking external field tends to zero in the thermodynamic limit. On the critical line there is also abnormal behavior, but the dependence on the way the field disappears, is slightly different. For densities below the critical density, the fluctuations are normal and independent of the way the external field goes to zero.
The exactness of the Bogoliubov approximation is discussed from the point of view of the condensation properties of the Bose gas. For the imperfect Bose gas, the authors find that the approximation yields the correct condensate density when the thermodynamic limit is taken by isotropic dilation; this is not the case in general for other ways of going to the infinite volume limit. They also prove the existence of Bose-Einstein condensation for a class of Bose gases with weak interactions and an energy gap.
Based on the canonical ensemble, we suggested the simple scheme for taking into account Gaussian fluctuations in a finite system of ideal boson gas. Within framework of scheme we investigated the influence of fluctuations on the particle distribution in Bose -gas for two cases - with taking into account the number of particles in the ground state and without this assumption. The temperature and fluctuation parameter dependences of the modified Bose-Einstein distribution have been determined. Also the dependence of the condensation temperature on the fluctuation distribution parameter has been obtained.